First slide

Motion of planets and satellites

Question

The orbital velocity of an artificial satellite in a circular orbit just above the earth's surface is v. For a satellite orbiting at an altitude of half of the earth's radius, the orbital velocity is

Moderate

A

$\frac{3}{2} v$
B

$\sqrt{\frac{3}{2}} v$
C

$\sqrt{\frac{2}{3}} v$
D

$\frac{2}{3} v$

Solution

$v = \sqrt{\frac{GM}{R + h}}$
$For first satellite h = 0, v_{1} = \sqrt{\frac{GM}{R}}$
$For second satellite h = \frac{R}{2}, v_{2} = \sqrt{\frac{2 GM}{3 R}}$
$v_{2} = \sqrt{\frac{2}{3}} v_{1} = \sqrt{\frac{2}{3}} v$

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